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Questions tagged [quantifiers]

The quantifiers $\forall$ ("for all") and $\exists$ ("there exists") distinguish predicate calculus from propositional logic.

Quantifiers specify the quantity of objects that satisfy a given formula.

The quantifiers $\forall$ (for all) and $\exists$ (there exists) are the most common, but others such as $\exists!$ (there exists a unique) are also in usage.

Only use this tag if your question is about the usage of a quantifier in a formula. Be sure not to use this tag for any question with quantifiers.

1826 questions
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Universal and Existential Quantifiers - Variables as Natural Numbers

It is said that an proposition with a universal quantifier represents a possibly infinite conjunction, and a proposition with an existential quantifier a possibly infinite disjunction. How can one illustrate this approach, where the quantified…
user670177
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Quantifiers- universal and existential

Let P(x) denote the statement “x is an accountant let Q(x) denote the statement “x owns a Porsche Someone who owns a Porsche is an accountant why is the answer ∃x (P(x) ^ Q(x)) and not ∃x (Q(x) -> P(X))?
Ryan gomez
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Quantifier difference

What s the difference between $ n \in Z \implies n(n+1) =2k $ such that $k \in Z$ and $ \forall n \in Z \implies n(n+1) =2k $ such that $k \in Z$ Is this true: $ (n \in Z \implies n(n+1) =2k $ such that $k \in Z) \implies \forall n \in Z; n(n+1) =2k…
Papa
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Difference between mentioning existential quantifier and not

Let $n \in N$, Is there a difference between: 1) let us assume as true $\exists k \in Z / n= 9 k$ and 2) let us assume as true $ n = 9k / k \in Z$?
Papa
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Quantifiers and variable link

I have asked a professor about the difference between the two expressions, he said the following: $\forall x, \exists y, \; p(x,y)$: y is linked to x $ \exists x,\forall y, \; p(x,y)$: y is not linked to x can you elaborate more on this?
Papa
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Interpretation of top and bottom concepts in the scope of quantifiers in description logics

What is the difference in interpretation of concepts: $\exists R.\top$, $\exists R.\bot$, $\forall R.\top$, $\forall R.\bot$? For instance, if we assume R means hasChild, will $\exists R.\top$ denote all individuals that have a child? And what would…
dpprosk
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Given any x in I and positive epsilon

I need to write the statement "Given any x in I and positive epsilon" symbolically. What is confusing is I know you can't the same variable for two different quantifiers and I don't think I can say I∈x ε∈x. Can anyone help clear this up for me?
George
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Write the following logical statement symbolically

I was given "If $f'(x)>0$ for every $x\in(a, b),$ then $f$ is increasing on $[a, b].$" and I need to write it out symbolically. I have gotten $$∀x\in(a,b) ~(f'(x)>0)\to (x0$ in more basic terms…
George
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Express the definition of prime in the language of quantifiers. Then state the negation in quantities, and interpret it in your own words

Here is my draft of Answer. Suppose p is a prime number, P€N and p not equal to1, and for all a€N, for all b € N, if P=a•b then a =1 or b=1 My questions: 1. Do I express the definition of prime in the language of quantifiers correctly? And how to…
Leir Leir
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Quantifiable statements question, is the statement true or false?!

The given quantified statement is: $\forall p \in \P_3, \forall q \in \P_3, p-q \in \P_3.$ ($\P_3$ stands for "third degree polynomial") The question asks to state if the original is true or false. I negated the statement to be: $\exists p \in…
futuremathteach
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Quantifier evaluation using translation to english

Which one of the following well-formed formulae is a tautology? $\hspace {2pt}$ a)$\forall x \exists y R(x,y) \leftrightarrow \exists y \forall x R(x,y) $ $\hspace{2pt}$b)$\forall x[\exists y\hspace{1pt} R(x,y)\rightarrow S(x,y)]\rightarrow \forall…
Curious
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Deciding between logical AND (conjunction) and Conditional statement

Hi I'm currently working through the book "How to Prove It" by Daniel Velleman and I'm having some trouble choosing between the conjunction and conditional statement when constructing logical statements. The most recent issue I had is when solving a…
skippy130
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Truth Statement of a domain

$\exists \ x \ \forall \ y\ (x\leq y^2)$ $\mathbb{N}:$ True $\mathbb{Z}:$ True $\mathbb{R}^+:$ False I understand why it is true with natural numbers and integers, but why is it false for the set of positive real numbers? What is an example of…
QuestionQuestion
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Using an Euler diagram determine if the argument is valid or invalid?

Some psychologists are university professors Some psychologists have a private practice Some university professors have private practice P.S. So I got the diagram which is 3 circles each representing psychologists, university professors and those…
Kristina Utas
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How does one write this in quantifiers?

A bounded sequence that is either strictly increasing or strictly decreasing, then it must converge to some limit. Thank you
yre
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